Theorem hbaes 1146

Description: Rule that applies hbae 1145 to antecedent.

Hypothesis

Ref	Expression
hbalequs.1	|- (A.zA.x x = y -> ph)

Assertion

Ref	Expression
hbaes	|- (A.x x = y -> ph)

Proof of Theorem hbaes

Step	Hyp	Ref	Expression
1		hbae 1145	. 2 |- (A.x x = y -> A.zA.x x = y)
2		hbalequs.1	. 2 |- (A.zA.x x = y -> ph)
3	1, 2	syl 10	1 |- (A.x x = y -> ph)

Syntax hints:   -> wi 3  A.wal 954   = wceq 956

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-10 966  ax-12 968  ax-4 973  ax-5o 975  ax-10o 1140

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